The Divine Proportion by H. E. Huntley

Author:H. E. Huntley
Language: eng
Format: epub
Publisher: Dover Publications, Inc.
Published: 2013-06-26T16:00:00+00:00

INGREDIENTS OF BEAUTY

Beauty in mathematics, as in music, is not elemental; it is a compound of several ingredients, which are not found in isolation—ingredients which have this in common: they stir buried memories which rise to awaken feelings in the conscious levels of the mind. Let us consider some of these. They are of a very general character, inherited by every member of the human race.

The alternation of tension and relief is a universal emotion. In reading any form of serious mathematics, we experience alternately perplexity and illumination. Out of chaos comes order. Out of the many, the one. This, reaching the deepest levels of feeling, gently stimulates the aesthetic sensibilities. The effect is found in music when the alternation in (e.g.) a hymn tune of the dominant and the tonic—tension and relaxation—contributes to the beauty of the tune. Another example is the familiar one of resolution of discord into harmony.

In mathematics a student who finds himself bewildered by the wide variety of the series representations of such functions as ex, log x, cos x etc., is delighted to find a theorem like Taylor’s which covers them all. “A beautiful generalization” may well be his reaction.

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